Journal of Formalized Mathematics
Volume 14, 2002
University of Bialystok
Copyright (c) 2002 Association of Mizar Users

## On the Decompositions of Intervals and Simple Closed Curves

University of Bialystok

### Summary.

The aim of the paper is to show that the only subcontinua of the Jordan curve are arcs, the whole curve, and singletons of its points. Additionally, it has been shown that the only subcontinua of the unit interval \$\Bbb I\$ are closed intervals.

This work has been partially supported by the European Community TYPES grant IST-1999-29001 and CALCULEMUS grant HPRN-CT-2000-00102.

#### MML Identifier: BORSUK_4

The terminology and notation used in this paper have been introduced in the following articles [23] [26] [1] [25] [27] [3] [5] [2] [4] [21] [8] [6] [22] [10] [12] [13] [17] [28] [20] [24] [15] [16] [18] [19] [11] [7] [14] [9]

#### Contents (PDF format)

1. Preliminaries
2. Decompositions of Intervals
3. Decompositions of Simple Closed Curves

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